Applied Math 254: Computer Networks

Slides/Notes for Class 4: Computer Network Topology

Mario A. Gerla (Network Analysis Corporation)

March 1975

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. TRAFFIC LOAD OF PRESENT ARPANET

A.1 TRAFFIC ANALYSIS .

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LIME COST- 5922M O D E M S - . 4,990C O N D I T I O N I N G - '2GGTERMINATION- 560

TOTAL 11.733 S/MONTHDELAY ATNOMINAL TRAFFIC • .408 SEC

6-21. Phase I - Topology 1

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TOTAL 14,950 S/MONTHDELAY ATNOMINAL TRAFFIC « 3 t4SEC

PNC " -003

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ALL LINES 9.6 KB/S

Figure 6-27. Phase I - Topology 4

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f° : STARTING FLOW? : LOCAL MINIMUM

Figure 5.6.2. Illustration of the FD Method.

Let us now investigate the effectiveness of DisCap in the

determination of the global minimum.

First of all, notice that the global minimum (f*,D*) is in

general not unique; more precisely, the optimal assignment C* is

unique (excluding pathological cases), but more than one flow f* does

in general satisfy T(f*,C*) <T . However, there is at least one** **» *"~ in 3.x

global solution (namely (f,C*), s.t. T(f,C*3 = min T(f,C*)) which is

also local, according to the previous definition.

DisCap finds local minima (which depend on the initial flow

f ) and therefore can determine the global minimum, if an appropriate

initial solution is chosen. Several initial flows can be generated and

several locals found with the random procedure described in Section 5.6;

141

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4ASSIGN LENGTHS «j

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ICOMPUTE SH ROUTEFLOW f°

APPLY FD ALGORITM

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ISELECT THE MINIMUM OF

THE LOCAL MINiMA

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Figurt 5 8 2b. Powar Le*t Approximation of Dbcrtt* Chonnel Cost* (Pert 2).

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3Si i . The results of the six runs are shewn in Tables S-8 5 to S.8.10.

For each run we give:\ cost of the best loc&l Kin: D ,

• . . ni n- distribution of the costs of the local oiniaa

I - ranCe of the .costs: « - °°"' D»in

Bin

where D is th« highest costMX

- relative cost improvement: e » ——^ —I Ufin

where D. is the initial cost end D- the final costin finfor th© best local runicaia '

of FD iterations psr local isiniauai

of arcs in the final topology

TABLE 5.6.5

KET A. && I (a. P

- Distribution of the coses:

D|$/nont.h] No. of solutions

88.400 - C8.SCO S

68,500 - £8,600 11

CS.600 - 03,700 11

GS.700 - 88, GOO 19

8S.EOO - gQ .000 _ 1

c « n . .ft • 12%

Number cf F^> I tcr t t iws f-"- eech local tain: 5 to 10. . . . - •

Number of «rcs in tne tin*! tro^t; rost' V v ' "'(including th« beat) have 31 arc*. ~*,a »ol.»t '^fts h«u« iO arcs.

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- Dis t r ibu t ion of the costs:

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68,000 -

69,000 -

70,000 -

71,000 -

72,000 -

75,000 -

64,000

68,000

69 ,000

70,000

71,000

72,000

73,000

74,000

Number ofsolutions

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TABLE S. ,8 .6

K'ET A. RUN 2 (a - 0,S) ^^ j!_J» «» W *

- 0 • 171

- e « 20%

- Number of FO iterations for each local Bin: 5 ro 13

- Nucber of arcs in the final topology: 27 to 30

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D « CONST

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-VD £

D = CONST

B) SMALL a (HIGH CURVATURE OF D = CONST LEVEL CURVES):4 LOCAL MINIF^A. WITH VERY DIFFERENT VALUES OF D

Figure 5811 Geometric Interpretation of tha Dependence of Numtwr endDiJtributicn of Local Minims -from a

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TABLE 6.6.1

COST DDISC AM5 TRAFFIC LOAD o FORVARIOUS 26 i<ODE ARPA TOPOLOGIES

HAKS | DDISC J

[

Fully conn. < 89,559 :

JAM ; 94,228 1

J03S i 94,314 jKAX3T - i 94.357 j

Hi£h.conn.l ! 55,191 jELS j 95,621 i

T031 96,017 ;

CAZ 1 £7,100 ];

Hig^.cona.2 t 97.215 !.KAC ! 97,2^0 iBAH ' 98, OSS iD£C2 ; SS.478 IDFO ; 98.SS4 ;

JC?2 i 99. 7831

TG2 - C-9,f-92 ;

K&S2 100,207 •' VCG i 100,815 1RJ3 101,075 !

• dtll ' 101,703 (i

D/^2 103,164 :K&X2 103,571 .

1

Am • 105,652 ',L «MI • . M ^MMII • mm !>• Ill 1 1 • 1 • '• • IM f II HIM

M\ i 105, C401 *

, LAS • 10S.540BU5 j 108,644JO? } 112,659Q1S 118.579KL£2 122,203DGCIP 1S3.251 ;DGC 141. £25 j

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p ' DCCXT . DCO:-.T.. HAn Irun disc : 0 •i

1.05 82,533 66,164 , 525 i* 1

1.00 03,792 68,709 ; 29

1.00 64.SS1 £6,154 551.05 68,877 83, £92 29 j

1.01 1 C2.149 62,466 41 1i i1.04 • S9,4£S 30,529 : 51 I

1.03 ! 89,154 69,154 ! 29

l.CO 03,537 i 88.S97 59 '1

1.02 £2,765 i 02,991 41I

1.03 85,006 " 83,006 341.C2 50,351 ; 91,427 S3l.CS 87,35,0 j 87,£SO S31.10 85.616 ' £6,616 55

}

1.03 88,405 i £8,764 , 51;

1.06 87,513 ; 87,574 S3

l.CO C&.7.S8 i 87,019 SOi1.03 G5,^)2 92,354 55

1

1.00 86.014 1 £6,614 551.C6 84.078 j 84,874 511.01 67.181 91,427 341.00 67,506 '' 87,728 55

'1.05 C4.6&0 87.SS9 34

1.00 i 29,270 •' 97,336 55i

1.10 ! SO.m , 90,124 i 51l.CO ! C7,£03 1 97, £41 ! 42

! ik.CO C3,941 : 91,602 , 541,00 , 91,556 I 94,553 5031.01 I SO, 470 50,431 291.03 £3,531 89,591 | 291.10 CO, 247 90,431 i 281.10 92,C91 i 92,991 . 51

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Figure 6,6.3 Second Best Solution: DD1SC - 94,288, p = 1.00

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O THE LOWER BOUND CORRESPONDS TOCONTINUOUS.u FITTED SOLUTIONS

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Figure 6.6 4b. Thruput p versus Cost D M Some Discrete Solutions Obtained m the Range p * 0.5 1 1.

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